LMFDB - Embedded newform 6034.2.a.m.1.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [6034,2,Mod(1,6034)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(6034, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 0]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("6034.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 6034 = 2 \cdot 7 \cdot 431 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	6034.a (trivial)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	yes
Analytic conductor:	$48.1817325796$
Analytic rank:	$1$
Dimension:	$21$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.7
Character	$\chi$	$=$	6034.1

$q$-expansion

comment: q-expansion

sage: f.q_expansion() # note that sage often uses an isomorphic number field

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000 q^{2} -1.49715 q^{3} +1.00000 q^{4} -0.207716 q^{5} -1.49715 q^{6} +1.00000 q^{7} +1.00000 q^{8} -0.758538 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} -1.49715 q^{3} +1.00000 q^{4} -0.207716 q^{5} -1.49715 q^{6} +1.00000 q^{7} +1.00000 q^{8} -0.758538 q^{9} -0.207716 q^{10} +1.25281 q^{11} -1.49715 q^{12} -1.61477 q^{13} +1.00000 q^{14} +0.310982 q^{15} +1.00000 q^{16} +0.634787 q^{17} -0.758538 q^{18} -0.170087 q^{19} -0.207716 q^{20} -1.49715 q^{21} +1.25281 q^{22} -2.22675 q^{23} -1.49715 q^{24} -4.95685 q^{25} -1.61477 q^{26} +5.62710 q^{27} +1.00000 q^{28} +8.15894 q^{29} +0.310982 q^{30} -6.40248 q^{31} +1.00000 q^{32} -1.87565 q^{33} +0.634787 q^{34} -0.207716 q^{35} -0.758538 q^{36} -11.2737 q^{37} -0.170087 q^{38} +2.41755 q^{39} -0.207716 q^{40} +10.0239 q^{41} -1.49715 q^{42} +3.93091 q^{43} +1.25281 q^{44} +0.157560 q^{45} -2.22675 q^{46} -3.91930 q^{47} -1.49715 q^{48} +1.00000 q^{49} -4.95685 q^{50} -0.950372 q^{51} -1.61477 q^{52} -10.1614 q^{53} +5.62710 q^{54} -0.260229 q^{55} +1.00000 q^{56} +0.254647 q^{57} +8.15894 q^{58} -5.56896 q^{59} +0.310982 q^{60} +3.23438 q^{61} -6.40248 q^{62} -0.758538 q^{63} +1.00000 q^{64} +0.335413 q^{65} -1.87565 q^{66} -2.95172 q^{67} +0.634787 q^{68} +3.33378 q^{69} -0.207716 q^{70} -9.79690 q^{71} -0.758538 q^{72} +16.4976 q^{73} -11.2737 q^{74} +7.42116 q^{75} -0.170087 q^{76} +1.25281 q^{77} +2.41755 q^{78} -6.59227 q^{79} -0.207716 q^{80} -6.14901 q^{81} +10.0239 q^{82} +1.90524 q^{83} -1.49715 q^{84} -0.131855 q^{85} +3.93091 q^{86} -12.2152 q^{87} +1.25281 q^{88} -8.58664 q^{89} +0.157560 q^{90} -1.61477 q^{91} -2.22675 q^{92} +9.58548 q^{93} -3.91930 q^{94} +0.0353298 q^{95} -1.49715 q^{96} -13.0023 q^{97} +1.00000 q^{98} -0.950307 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 21 q + 21 q^{2} - 6 q^{3} + 21 q^{4} - 11 q^{5} - 6 q^{6} + 21 q^{7} + 21 q^{8} + 5 q^{9}+O(q^{10}) $ 21 * q + 21 * q^2 - 6 * q^3 + 21 * q^4 - 11 * q^5 - 6 * q^6 + 21 * q^7 + 21 * q^8 + 5 * q^9	\( 21 q + 21 q^{2} - 6 q^{3} + 21 q^{4} - 11 q^{5} - 6 q^{6} + 21 q^{7} + 21 q^{8} + 5 q^{9} - 11 q^{10} - 34 q^{11} - 6 q^{12} - 19 q^{13} + 21 q^{14} - 24 q^{15} + 21 q^{16} - 17 q^{17} + 5 q^{18} - 15 q^{19} - 11 q^{20} - 6 q^{21} - 34 q^{22} - 32 q^{23} - 6 q^{24} + 6 q^{25} - 19 q^{26} - 3 q^{27} + 21 q^{28} - 46 q^{29} - 24 q^{30} + 7 q^{31} + 21 q^{32} - 13 q^{33} - 17 q^{34} - 11 q^{35} + 5 q^{36} - 34 q^{37} - 15 q^{38} - 25 q^{39} - 11 q^{40} - 27 q^{41} - 6 q^{42} - 47 q^{43} - 34 q^{44} - 13 q^{45} - 32 q^{46} - 7 q^{47} - 6 q^{48} + 21 q^{49} + 6 q^{50} - 29 q^{51} - 19 q^{52} - 57 q^{53} - 3 q^{54} + 17 q^{55} + 21 q^{56} - 28 q^{57} - 46 q^{58} - 30 q^{59} - 24 q^{60} - 17 q^{61} + 7 q^{62} + 5 q^{63} + 21 q^{64} - 40 q^{65} - 13 q^{66} - 38 q^{67} - 17 q^{68} - 13 q^{69} - 11 q^{70} - 66 q^{71} + 5 q^{72} - 15 q^{73} - 34 q^{74} + 15 q^{75} - 15 q^{76} - 34 q^{77} - 25 q^{78} - 17 q^{79} - 11 q^{80} - 11 q^{81} - 27 q^{82} - 19 q^{83} - 6 q^{84} - 28 q^{85} - 47 q^{86} + 45 q^{87} - 34 q^{88} - 39 q^{89} - 13 q^{90} - 19 q^{91} - 32 q^{92} - 25 q^{93} - 7 q^{94} - 35 q^{95} - 6 q^{96} + 21 q^{98} - 52 q^{99}+O(q^{100}) \) 21 * q + 21 * q^2 - 6 * q^3 + 21 * q^4 - 11 * q^5 - 6 * q^6 + 21 * q^7 + 21 * q^8 + 5 * q^9 - 11 * q^10 - 34 * q^11 - 6 * q^12 - 19 * q^13 + 21 * q^14 - 24 * q^15 + 21 * q^16 - 17 * q^17 + 5 * q^18 - 15 * q^19 - 11 * q^20 - 6 * q^21 - 34 * q^22 - 32 * q^23 - 6 * q^24 + 6 * q^25 - 19 * q^26 - 3 * q^27 + 21 * q^28 - 46 * q^29 - 24 * q^30 + 7 * q^31 + 21 * q^32 - 13 * q^33 - 17 * q^34 - 11 * q^35 + 5 * q^36 - 34 * q^37 - 15 * q^38 - 25 * q^39 - 11 * q^40 - 27 * q^41 - 6 * q^42 - 47 * q^43 - 34 * q^44 - 13 * q^45 - 32 * q^46 - 7 * q^47 - 6 * q^48 + 21 * q^49 + 6 * q^50 - 29 * q^51 - 19 * q^52 - 57 * q^53 - 3 * q^54 + 17 * q^55 + 21 * q^56 - 28 * q^57 - 46 * q^58 - 30 * q^59 - 24 * q^60 - 17 * q^61 + 7 * q^62 + 5 * q^63 + 21 * q^64 - 40 * q^65 - 13 * q^66 - 38 * q^67 - 17 * q^68 - 13 * q^69 - 11 * q^70 - 66 * q^71 + 5 * q^72 - 15 * q^73 - 34 * q^74 + 15 * q^75 - 15 * q^76 - 34 * q^77 - 25 * q^78 - 17 * q^79 - 11 * q^80 - 11 * q^81 - 27 * q^82 - 19 * q^83 - 6 * q^84 - 28 * q^85 - 47 * q^86 + 45 * q^87 - 34 * q^88 - 39 * q^89 - 13 * q^90 - 19 * q^91 - 32 * q^92 - 25 * q^93 - 7 * q^94 - 35 * q^95 - 6 * q^96 + 21 * q^98 - 52 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$	$a_n / n^{(k-1)/2}$	$ \alpha_n $			$ \theta_n $
$p$	$a_p$	$a_p / p^{(k-1)/2}$	$ \alpha_p$			$ \theta_p $

$2$	1.00000	0.707107
$2$	1.00000	0.707107
$3$	−1.49715	−0.864381	−0.432190	−	0.901782i	$-0.642259\pi$
$3$	−1.49715	−0.864381	−0.432190	+	0.901782i	$0.642259\pi$
$4$	1.00000	0.500000
$5$	−0.207716	−0.0928933	−0.0464467	−	0.998921i	$-0.514790\pi$
$5$	−0.207716	−0.0928933	−0.0464467	+	0.998921i	$0.514790\pi$
$6$	−1.49715	−0.611209
$7$	1.00000	0.377964
$7$	1.00000	0.377964
$8$	1.00000	0.353553
$9$	−0.758538	−0.252846
$10$	−0.207716	−0.0656855
$11$	1.25281	0.377738	0.188869	−	0.982002i	$-0.439518\pi$
$11$	1.25281	0.377738	0.188869	+	0.982002i	$0.439518\pi$
$12$	−1.49715	−0.432190
$13$	−1.61477	−0.447856	−0.223928	−	0.974606i	$-0.571888\pi$
$13$	−1.61477	−0.447856	−0.223928	+	0.974606i	$0.571888\pi$
$14$	1.00000	0.267261
$15$	0.310982	0.0802952
$16$	1.00000	0.250000
$17$	0.634787	0.153958	0.0769792	−	0.997033i	$-0.475472\pi$
$17$	0.634787	0.153958	0.0769792	+	0.997033i	$0.475472\pi$
$18$	−0.758538	−0.178789
$19$	−0.170087	−0.0390207	−0.0195104	−	0.999810i	$-0.506211\pi$
$19$	−0.170087	−0.0390207	−0.0195104	+	0.999810i	$0.506211\pi$
$20$	−0.207716	−0.0464467
$21$	−1.49715	−0.326705
$22$	1.25281	0.267101
$23$	−2.22675	−0.464309	−0.232155	−	0.972679i	$-0.574578\pi$
$23$	−2.22675	−0.464309	−0.232155	+	0.972679i	$0.574578\pi$
$24$	−1.49715	−0.305605
$25$	−4.95685	−0.991371
$26$	−1.61477	−0.316682
$27$	5.62710	1.08294
$28$	1.00000	0.188982
$29$	8.15894	1.51508	0.757539	−	0.652790i	$-0.226402\pi$
$29$	8.15894	1.51508	0.757539	+	0.652790i	$0.226402\pi$
$30$	0.310982	0.0567773
$31$	−6.40248	−1.14992	−0.574960	−	0.818182i	$-0.694982\pi$
$31$	−6.40248	−1.14992	−0.574960	+	0.818182i	$0.694982\pi$
$32$	1.00000	0.176777
$33$	−1.87565	−0.326509
$34$	0.634787	0.108865
$35$	−0.207716	−0.0351104
$36$	−0.758538	−0.126423
$37$	−11.2737	−1.85338	−0.926689	−	0.375830i	$-0.877358\pi$
$37$	−11.2737	−1.85338	−0.926689	+	0.375830i	$0.877358\pi$
$38$	−0.170087	−0.0275918
$39$	2.41755	0.387118
$40$	−0.207716	−0.0328427
$41$	10.0239	1.56546	0.782732	−	0.622359i	$-0.213826\pi$
$41$	10.0239	1.56546	0.782732	+	0.622359i	$0.213826\pi$
$42$	−1.49715	−0.231015
$43$	3.93091	0.599458	0.299729	−	0.954024i	$-0.403104\pi$
$43$	3.93091	0.599458	0.299729	+	0.954024i	$0.403104\pi$
$44$	1.25281	0.188869
$45$	0.157560	0.0234877
$46$	−2.22675	−0.328316
$47$	−3.91930	−0.571689	−0.285844	−	0.958276i	$-0.592274\pi$
$47$	−3.91930	−0.571689	−0.285844	+	0.958276i	$0.592274\pi$
$48$	−1.49715	−0.216095
$49$	1.00000	0.142857
$50$	−4.95685	−0.701005
$51$	−0.950372	−0.133079
$52$	−1.61477	−0.223928
$53$	−10.1614	−1.39578	−0.697890	−	0.716205i	$-0.745878\pi$
$53$	−10.1614	−1.39578	−0.697890	+	0.716205i	$0.745878\pi$
$54$	5.62710	0.765751
$55$	−0.260229	−0.0350893
$56$	1.00000	0.133631
$57$	0.254647	0.0337288
$58$	8.15894	1.07132
$59$	−5.56896	−0.725017	−0.362509	−	0.931980i	$-0.618080\pi$
$59$	−5.56896	−0.725017	−0.362509	+	0.931980i	$0.618080\pi$
$60$	0.310982	0.0401476
$61$	3.23438	0.414119	0.207060	−	0.978328i	$-0.433611\pi$
$61$	3.23438	0.414119	0.207060	+	0.978328i	$0.433611\pi$
$62$	−6.40248	−0.813116
$63$	−0.758538	−0.0955668
$64$	1.00000	0.125000
$65$	0.335413	0.0416028
$66$	−1.87565	−0.230877
$67$	−2.95172	−0.360610	−0.180305	−	0.983611i	$-0.557709\pi$
$67$	−2.95172	−0.360610	−0.180305	+	0.983611i	$0.557709\pi$
$68$	0.634787	0.0769792
$69$	3.33378	0.401340
$70$	−0.207716	−0.0248268
$71$	−9.79690	−1.16268	−0.581339	−	0.813661i	$-0.697471\pi$
$71$	−9.79690	−1.16268	−0.581339	+	0.813661i	$0.697471\pi$
$72$	−0.758538	−0.0893945
$73$	16.4976	1.93090	0.965451	−	0.260586i	$-0.0839159\pi$
$73$	16.4976	1.93090	0.965451	+	0.260586i	$0.0839159\pi$
$74$	−11.2737	−1.31054
$75$	7.42116	0.856922
$76$	−0.170087	−0.0195104
$77$	1.25281	0.142771
$78$	2.41755	0.273734
$79$	−6.59227	−0.741688	−0.370844	−	0.928695i	$-0.620932\pi$
$79$	−6.59227	−0.741688	−0.370844	+	0.928695i	$0.620932\pi$
$80$	−0.207716	−0.0232233
$81$	−6.14901	−0.683223
$82$	10.0239	1.10695
$83$	1.90524	0.209127	0.104564	−	0.994518i	$-0.466655\pi$
$83$	1.90524	0.209127	0.104564	+	0.994518i	$0.466655\pi$
$84$	−1.49715	−0.163353
$85$	−0.131855	−0.0143017
$86$	3.93091	0.423881
$87$	−12.2152	−1.30960
$88$	1.25281	0.133550
$89$	−8.58664	−0.910182	−0.455091	−	0.890445i	$-0.650393\pi$
$89$	−8.58664	−0.910182	−0.455091	+	0.890445i	$0.650393\pi$
$90$	0.157560	0.0166083
$91$	−1.61477	−0.169274
$92$	−2.22675	−0.232155
$93$	9.58548	0.993968
$94$	−3.91930	−0.404245
$95$	0.0353298	0.00362476
$96$	−1.49715	−0.152802
$97$	−13.0023	−1.32018	−0.660092	−	0.751185i	$-0.729483\pi$
$97$	−13.0023	−1.32018	−0.660092	+	0.751185i	$0.729483\pi$
$98$	1.00000	0.101015
$99$	−0.950307	−0.0955094
$100$	−4.95685	−0.495685
$101$	−0.775970	−0.0772119	−0.0386060	−	0.999255i	$-0.512292\pi$
$101$	−0.775970	−0.0772119	−0.0386060	+	0.999255i	$0.512292\pi$
$102$	−0.950372	−0.0941009
$103$	16.3224	1.60829	0.804145	−	0.594433i	$-0.202623\pi$
$103$	16.3224	1.60829	0.804145	+	0.594433i	$0.202623\pi$
$104$	−1.61477	−0.158341
$105$	0.310982	0.0303487
$106$	−10.1614	−0.986966
$107$	4.60592	0.445271	0.222636	−	0.974902i	$-0.428534\pi$
$107$	4.60592	0.445271	0.222636	+	0.974902i	$0.428534\pi$
$108$	5.62710	0.541468
$109$	−17.8248	−1.70731	−0.853655	−	0.520838i	$-0.825619\pi$
$109$	−17.8248	−1.70731	−0.853655	+	0.520838i	$0.825619\pi$
$110$	−0.260229	−0.0248119
$111$	16.8784	1.60202
$112$	1.00000	0.0944911
$113$	−0.444278	−0.0417942	−0.0208971	−	0.999782i	$-0.506652\pi$
$113$	−0.444278	−0.0417942	−0.0208971	+	0.999782i	$0.506652\pi$
$114$	0.254647	0.0238498
$115$	0.462531	0.0431312
$116$	8.15894	0.757539
$117$	1.22486	0.113239
$118$	−5.56896	−0.512664
$119$	0.634787	0.0581908
$120$	0.310982	0.0283886
$121$	−9.43046	−0.857314
$122$	3.23438	0.292827
$123$	−15.0072	−1.35316
$124$	−6.40248	−0.574960
$125$	2.06820	0.184985
$126$	−0.758538	−0.0675759
$127$	4.52306	0.401356	0.200678	−	0.979657i	$-0.435685\pi$
$127$	4.52306	0.401356	0.200678	+	0.979657i	$0.435685\pi$
$128$	1.00000	0.0883883
$129$	−5.88517	−0.518160
$130$	0.335413	0.0294176
$131$	5.04659	0.440922	0.220461	−	0.975396i	$-0.429244\pi$
$131$	5.04659	0.440922	0.220461	+	0.975396i	$0.429244\pi$
$132$	−1.87565	−0.163255
$133$	−0.170087	−0.0147484
$134$	−2.95172	−0.254990
$135$	−1.16884	−0.100597
$136$	0.634787	0.0544325
$137$	−7.20198	−0.615306	−0.307653	−	0.951499i	$-0.599544\pi$
$137$	−7.20198	−0.615306	−0.307653	+	0.951499i	$0.599544\pi$
$138$	3.33378	0.283790
$139$	−17.9823	−1.52524	−0.762618	−	0.646849i	$-0.776086\pi$
$139$	−17.9823	−1.52524	−0.762618	+	0.646849i	$0.776086\pi$
$140$	−0.207716	−0.0175552
$141$	5.86779	0.494157
$142$	−9.79690	−0.822138
$143$	−2.02300	−0.169172
$144$	−0.758538	−0.0632115
$145$	−1.69474	−0.140741
$146$	16.4976	1.36535
$147$	−1.49715	−0.123483
$148$	−11.2737	−0.926689
$149$	8.65050	0.708677	0.354338	−	0.935117i	$-0.384706\pi$
$149$	8.65050	0.708677	0.354338	+	0.935117i	$0.384706\pi$
$150$	7.42116	0.605935
$151$	4.81532	0.391865	0.195933	−	0.980617i	$-0.437227\pi$
$151$	4.81532	0.391865	0.195933	+	0.980617i	$0.437227\pi$
$152$	−0.170087	−0.0137959
$153$	−0.481510	−0.0389278
$154$	1.25281	0.100955
$155$	1.32990	0.106820
$156$	2.41755	0.193559
$157$	7.87450	0.628454	0.314227	−	0.949348i	$-0.398255\pi$
$157$	7.87450	0.628454	0.314227	+	0.949348i	$0.398255\pi$
$158$	−6.59227	−0.524453
$159$	15.2132	1.20649
$160$	−0.207716	−0.0164214
$161$	−2.22675	−0.175492
$162$	−6.14901	−0.483112
$163$	−25.4553	−1.99382	−0.996908	−	0.0785795i	$-0.974962\pi$
$163$	−25.4553	−1.99382	−0.996908	+	0.0785795i	$0.974962\pi$
$164$	10.0239	0.782732
$165$	0.389603	0.0303305
$166$	1.90524	0.147875
$167$	4.20396	0.325313	0.162656	−	0.986683i	$-0.447994\pi$
$167$	4.20396	0.325313	0.162656	+	0.986683i	$0.447994\pi$
$168$	−1.49715	−0.115508
$169$	−10.3925	−0.799425
$170$	−0.131855	−0.0101128
$171$	0.129018	0.00986623
$172$	3.93091	0.299729
$173$	−11.2423	−0.854739	−0.427370	−	0.904077i	$-0.640560\pi$
$173$	−11.2423	−0.854739	−0.427370	+	0.904077i	$0.640560\pi$
$174$	−12.2152	−0.926030
$175$	−4.95685	−0.374703
$176$	1.25281	0.0944344
$177$	8.33758	0.626691
$178$	−8.58664	−0.643596
$179$	7.60389	0.568341	0.284171	−	0.958774i	$-0.408282\pi$
$179$	7.60389	0.568341	0.284171	+	0.958774i	$0.408282\pi$
$180$	0.157560	0.0117438
$181$	3.61024	0.268347	0.134174	−	0.990958i	$-0.457162\pi$
$181$	3.61024	0.268347	0.134174	+	0.990958i	$0.457162\pi$
$182$	−1.61477	−0.119695
$183$	−4.84235	−0.357957
$184$	−2.22675	−0.164158
$185$	2.34172	0.172166
$186$	9.58548	0.702842
$187$	0.795270	0.0581559
$188$	−3.91930	−0.285844
$189$	5.62710	0.409311
$190$	0.0353298	0.00256309
$191$	−8.85791	−0.640936	−0.320468	−	0.947259i	$-0.603840\pi$
$191$	−8.85791	−0.640936	−0.320468	+	0.947259i	$0.603840\pi$
$192$	−1.49715	−0.108048
$193$	−3.93886	−0.283525	−0.141763	−	0.989901i	$-0.545277\pi$
$193$	−3.93886	−0.283525	−0.141763	+	0.989901i	$0.545277\pi$
$194$	−13.0023	−0.933511
$195$	−0.502164	−0.0359607
$196$	1.00000	0.0714286
$197$	22.9581	1.63570	0.817849	−	0.575433i	$-0.195166\pi$
$197$	22.9581	1.63570	0.817849	+	0.575433i	$0.195166\pi$
$198$	−0.950307	−0.0675354
$199$	−20.8529	−1.47822	−0.739112	−	0.673583i	$-0.764754\pi$
$199$	−20.8529	−1.47822	−0.739112	+	0.673583i	$0.764754\pi$
$200$	−4.95685	−0.350503
$201$	4.41917	0.311705
$202$	−0.775970	−0.0545971
$203$	8.15894	0.572646
$204$	−0.950372	−0.0665393
$205$	−2.08211	−0.145421
$206$	16.3224	1.13723
$207$	1.68907	0.117399
$208$	−1.61477	−0.111964
$209$	−0.213088	−0.0147396
$210$	0.310982	0.0214598
$211$	−23.2405	−1.59994	−0.799970	−	0.600039i	$-0.795152\pi$
$211$	−23.2405	−1.59994	−0.799970	+	0.600039i	$0.795152\pi$
$212$	−10.1614	−0.697890
$213$	14.6674	1.00500
$214$	4.60592	0.314854
$215$	−0.816512	−0.0556857
$216$	5.62710	0.382876
$217$	−6.40248	−0.434629
$218$	−17.8248	−1.20725
$219$	−24.6994	−1.66903
$220$	−0.260229	−0.0175447
$221$	−1.02503	−0.0689512
$222$	16.8784	1.13280
$223$	−6.15394	−0.412098	−0.206049	−	0.978542i	$-0.566061\pi$
$223$	−6.15394	−0.412098	−0.206049	+	0.978542i	$0.566061\pi$
$224$	1.00000	0.0668153
$225$	3.75996	0.250664
$226$	−0.444278	−0.0295529
$227$	−3.91162	−0.259623	−0.129812	−	0.991539i	$-0.541437\pi$
$227$	−3.91162	−0.259623	−0.129812	+	0.991539i	$0.541437\pi$
$228$	0.254647	0.0168644
$229$	2.86258	0.189164	0.0945822	−	0.995517i	$-0.469848\pi$
$229$	2.86258	0.189164	0.0945822	+	0.995517i	$0.469848\pi$
$230$	0.462531	0.0304984
$231$	−1.87565	−0.123409
$232$	8.15894	0.535661
$233$	−6.48488	−0.424839	−0.212419	−	0.977179i	$-0.568134\pi$
$233$	−6.48488	−0.424839	−0.212419	+	0.977179i	$0.568134\pi$
$234$	1.22486	0.0800718
$235$	0.814101	0.0531061
$236$	−5.56896	−0.362509
$237$	9.86962	0.641101
$238$	0.634787	0.0411471
$239$	16.8360	1.08903	0.544515	−	0.838751i	$-0.316714\pi$
$239$	16.8360	1.08903	0.544515	+	0.838751i	$0.316714\pi$
$240$	0.310982	0.0200738
$241$	2.12359	0.136793	0.0683964	−	0.997658i	$-0.478212\pi$
$241$	2.12359	0.136793	0.0683964	+	0.997658i	$0.478212\pi$
$242$	−9.43046	−0.606213
$243$	−7.67531	−0.492371
$244$	3.23438	0.207060
$245$	−0.207716	−0.0132705
$246$	−15.0072	−0.956826
$247$	0.274652	0.0174757
$248$	−6.40248	−0.406558
$249$	−2.85243	−0.180765
$250$	2.06820	0.130804
$251$	−4.50268	−0.284207	−0.142103	−	0.989852i	$-0.545387\pi$
$251$	−4.50268	−0.284207	−0.142103	+	0.989852i	$0.545387\pi$
$252$	−0.758538	−0.0477834
$253$	−2.78970	−0.175387
$254$	4.52306	0.283802
$255$	0.197407	0.0123621
$256$	1.00000	0.0625000
$257$	−19.9032	−1.24153	−0.620765	−	0.783997i	$-0.713178\pi$
$257$	−19.9032	−1.24153	−0.620765	+	0.783997i	$0.713178\pi$
$258$	−5.88517	−0.366395
$259$	−11.2737	−0.700511
$260$	0.335413	0.0208014
$261$	−6.18887	−0.383081
$262$	5.04659	0.311779
$263$	−4.59713	−0.283471	−0.141736	−	0.989905i	$-0.545268\pi$
$263$	−4.59713	−0.283471	−0.141736	+	0.989905i	$0.545268\pi$
$264$	−1.87565	−0.115438
$265$	2.11069	0.129659
$266$	−0.170087	−0.0104287
$267$	12.8555	0.786744
$268$	−2.95172	−0.180305
$269$	19.4403	1.18529	0.592647	−	0.805462i	$-0.298083\pi$
$269$	19.4403	1.18529	0.592647	+	0.805462i	$0.298083\pi$
$270$	−1.16884	−0.0711332
$271$	−13.0032	−0.789887	−0.394944	−	0.918705i	$-0.629236\pi$
$271$	−13.0032	−0.789887	−0.394944	+	0.918705i	$0.629236\pi$
$272$	0.634787	0.0384896
$273$	2.41755	0.146317
$274$	−7.20198	−0.435087
$275$	−6.21002	−0.374478
$276$	3.33378	0.200670
$277$	11.0275	0.662578	0.331289	−	0.943529i	$-0.392517\pi$
$277$	11.0275	0.662578	0.331289	+	0.943529i	$0.392517\pi$
$278$	−17.9823	−1.07850
$279$	4.85652	0.290752
$280$	−0.207716	−0.0124134
$281$	−32.6215	−1.94604	−0.973018	−	0.230729i	$-0.925889\pi$
$281$	−32.6215	−1.94604	−0.973018	+	0.230729i	$0.925889\pi$
$282$	5.86779	0.349422
$283$	−9.92705	−0.590102	−0.295051	−	0.955482i	$-0.595337\pi$
$283$	−9.92705	−0.590102	−0.295051	+	0.955482i	$0.595337\pi$
$284$	−9.79690	−0.581339
$285$	−0.0528941	−0.00313318
$286$	−2.02300	−0.119623
$287$	10.0239	0.591690
$288$	−0.758538	−0.0446973
$289$	−16.5970	−0.976297
$290$	−1.69474	−0.0995186
$291$	19.4664	1.14114
$292$	16.4976	0.965451
$293$	−23.8337	−1.39238	−0.696190	−	0.717858i	$-0.745123\pi$
$293$	−23.8337	−1.39238	−0.696190	+	0.717858i	$0.745123\pi$
$294$	−1.49715	−0.0873156
$295$	1.15676	0.0673492
$296$	−11.2737	−0.655268
$297$	7.04971	0.409066
$298$	8.65050	0.501110
$299$	3.59568	0.207944
$300$	7.42116	0.428461
$301$	3.93091	0.226574
$302$	4.81532	0.277090
$303$	1.16174	0.0667405
$304$	−0.170087	−0.00975518
$305$	−0.671831	−0.0384689
$306$	−0.481510	−0.0275261
$307$	−6.54022	−0.373270	−0.186635	−	0.982429i	$-0.559758\pi$
$307$	−6.54022	−0.373270	−0.186635	+	0.982429i	$0.559758\pi$
$308$	1.25281	0.0713857
$309$	−24.4370	−1.39018
$310$	1.32990	0.0755330
$311$	11.4769	0.650793	0.325397	−	0.945578i	$-0.394502\pi$
$311$	11.4769	0.650793	0.325397	+	0.945578i	$0.394502\pi$
$312$	2.41755	0.136867
$313$	3.51223	0.198523	0.0992614	−	0.995061i	$-0.468352\pi$
$313$	3.51223	0.198523	0.0992614	+	0.995061i	$0.468352\pi$
$314$	7.87450	0.444384
$315$	0.157560	0.00887751
$316$	−6.59227	−0.370844
$317$	−21.7537	−1.22181	−0.610905	−	0.791704i	$-0.709194\pi$
$317$	−21.7537	−1.22181	−0.610905	+	0.791704i	$0.709194\pi$
$318$	15.2132	0.853114
$319$	10.2216	0.572302
$320$	−0.207716	−0.0116117
$321$	−6.89576	−0.384884
$322$	−2.22675	−0.124092
$323$	−0.107969	−0.00600757
$324$	−6.14901	−0.341612
$325$	8.00417	0.443991
$326$	−25.4553	−1.40984
$327$	26.6865	1.47577
$328$	10.0239	0.553475
$329$	−3.91930	−0.216078
$330$	0.389603	0.0214469
$331$	−9.53912	−0.524317	−0.262159	−	0.965025i	$-0.584434\pi$
$331$	−9.53912	−0.524317	−0.262159	+	0.965025i	$0.584434\pi$
$332$	1.90524	0.104564
$333$	8.55149	0.468619
$334$	4.20396	0.230031
$335$	0.613119	0.0334983
$336$	−1.49715	−0.0816763
$337$	19.1447	1.04288	0.521439	−	0.853288i	$-0.325395\pi$
$337$	19.1447	1.04288	0.521439	+	0.853288i	$0.325395\pi$
$338$	−10.3925	−0.565279
$339$	0.665152	0.0361261
$340$	−0.131855	−0.00715085
$341$	−8.02112	−0.434368
$342$	0.129018	0.00697648
$343$	1.00000	0.0539949
$344$	3.93091	0.211941
$345$	−0.692479	−0.0372818
$346$	−11.2423	−0.604392
$347$	2.40424	0.129067	0.0645333	−	0.997916i	$-0.479444\pi$
$347$	2.40424	0.129067	0.0645333	+	0.997916i	$0.479444\pi$
$348$	−12.2152	−0.654802
$349$	13.6670	0.731578	0.365789	−	0.930698i	$-0.380799\pi$
$349$	13.6670	0.731578	0.365789	+	0.930698i	$0.380799\pi$
$350$	−4.95685	−0.264955
$351$	−9.08646	−0.484999
$352$	1.25281	0.0667752
$353$	−22.6032	−1.20305	−0.601523	−	0.798855i	$-0.705439\pi$
$353$	−22.6032	−1.20305	−0.601523	+	0.798855i	$0.705439\pi$
$354$	8.33758	0.443137
$355$	2.03497	0.108005
$356$	−8.58664	−0.455091
$357$	−0.950372	−0.0502990
$358$	7.60389	0.401878
$359$	31.8809	1.68261	0.841304	−	0.540563i	$-0.181789\pi$
$359$	31.8809	1.68261	0.841304	+	0.540563i	$0.181789\pi$
$360$	0.157560	0.00830415
$361$	−18.9711	−0.998477
$362$	3.61024	0.189750
$363$	14.1188	0.741046
$364$	−1.61477	−0.0846368
$365$	−3.42682	−0.179368
$366$	−4.84235	−0.253114
$367$	25.6929	1.34116	0.670578	−	0.741839i	$-0.266046\pi$
$367$	25.6929	1.34116	0.670578	+	0.741839i	$0.266046\pi$
$368$	−2.22675	−0.116077
$369$	−7.60347	−0.395821
$370$	2.34172	0.121740
$371$	−10.1614	−0.527555
$372$	9.58548	0.496984
$373$	−7.50515	−0.388602	−0.194301	−	0.980942i	$-0.562244\pi$
$373$	−7.50515	−0.388602	−0.194301	+	0.980942i	$0.562244\pi$
$374$	0.795270	0.0411224
$375$	−3.09640	−0.159897
$376$	−3.91930	−0.202123
$377$	−13.1748	−0.678537
$378$	5.62710	0.289427
$379$	23.2831	1.19597	0.597985	−	0.801507i	$-0.295968\pi$
$379$	23.2831	1.19597	0.597985	+	0.801507i	$0.295968\pi$
$380$	0.0353298	0.00181238
$381$	−6.77170	−0.346925
$382$	−8.85791	−0.453210
$383$	−6.85794	−0.350424	−0.175212	−	0.984531i	$-0.556061\pi$
$383$	−6.85794	−0.350424	−0.175212	+	0.984531i	$0.556061\pi$
$384$	−1.49715	−0.0764012
$385$	−0.260229	−0.0132625
$386$	−3.93886	−0.200483
$387$	−2.98175	−0.151571
$388$	−13.0023	−0.660092
$389$	−18.6914	−0.947693	−0.473847	−	0.880607i	$-0.657135\pi$
$389$	−18.6914	−0.947693	−0.473847	+	0.880607i	$0.657135\pi$
$390$	−0.502164	−0.0254280
$391$	−1.41351	−0.0714843
$392$	1.00000	0.0505076
$393$	−7.55551	−0.381125
$394$	22.9581	1.15661
$395$	1.36932	0.0688979
$396$	−0.950307	−0.0477547
$397$	−7.92237	−0.397612	−0.198806	−	0.980039i	$-0.563706\pi$
$397$	−7.92237	−0.397612	−0.198806	+	0.980039i	$0.563706\pi$
$398$	−20.8529	−1.04526
$399$	0.254647	0.0127483
$400$	−4.95685	−0.247843
$401$	−26.5403	−1.32536	−0.662681	−	0.748902i	$-0.730581\pi$
$401$	−26.5403	−1.32536	−0.662681	+	0.748902i	$0.730581\pi$
$402$	4.41917	0.220408
$403$	10.3385	0.514998
$404$	−0.775970	−0.0386060
$405$	1.27725	0.0634668
$406$	8.15894	0.404922
$407$	−14.1238	−0.700091
$408$	−0.950372	−0.0470504
$409$	29.1109	1.43944	0.719721	−	0.694264i	$-0.244270\pi$
$409$	29.1109	1.43944	0.719721	+	0.694264i	$0.244270\pi$
$410$	−2.08211	−0.102828
$411$	10.7824	0.531859
$412$	16.3224	0.804145
$413$	−5.56896	−0.274031
$414$	1.68907	0.0830134
$415$	−0.395748	−0.0194265
$416$	−1.61477	−0.0791705
$417$	26.9222	1.31838
$418$	−0.213088	−0.0104225
$419$	−35.5714	−1.73778	−0.868889	−	0.495008i	$-0.835165\pi$
$419$	−35.5714	−1.73778	−0.868889	+	0.495008i	$0.835165\pi$
$420$	0.310982	0.0151744
$421$	−30.6682	−1.49468	−0.747339	−	0.664443i	$-0.768669\pi$
$421$	−30.6682	−1.49468	−0.747339	+	0.664443i	$0.768669\pi$
$422$	−23.2405	−1.13133
$423$	2.97294	0.144549
$424$	−10.1614	−0.493483
$425$	−3.14655	−0.152630
$426$	14.6674	0.710640
$427$	3.23438	0.156522
$428$	4.60592	0.222636
$429$	3.02874	0.146229
$430$	−0.816512	−0.0393757
$431$	−1.00000	−0.0481683
$431$	−1.00000	−0.0481683
$432$	5.62710	0.270734
$433$	23.8209	1.14476	0.572379	−	0.819989i	$-0.306021\pi$
$433$	23.8209	1.14476	0.572379	+	0.819989i	$0.306021\pi$
$434$	−6.40248	−0.307329
$435$	2.53728	0.121653
$436$	−17.8248	−0.853655
$437$	0.378742	0.0181177
$438$	−24.6994	−1.18019
$439$	−30.5769	−1.45936	−0.729678	−	0.683791i	$-0.760330\pi$
$439$	−30.5769	−1.45936	−0.729678	+	0.683791i	$0.760330\pi$
$440$	−0.260229	−0.0124059
$441$	−0.758538	−0.0361208
$442$	−1.02503	−0.0487559
$443$	22.9515	1.09046	0.545229	−	0.838287i	$-0.316443\pi$
$443$	22.9515	1.09046	0.545229	+	0.838287i	$0.316443\pi$
$444$	16.8784	0.801012
$445$	1.78358	0.0845499
$446$	−6.15394	−0.291398
$447$	−12.9511	−0.612567
$448$	1.00000	0.0472456
$449$	−13.7725	−0.649963	−0.324982	−	0.945720i	$-0.605358\pi$
$449$	−13.7725	−0.649963	−0.324982	+	0.945720i	$0.605358\pi$
$450$	3.75996	0.177246
$451$	12.5580	0.591335
$452$	−0.444278	−0.0208971
$453$	−7.20926	−0.338721
$454$	−3.91162	−0.183582
$455$	0.335413	0.0157244
$456$	0.254647	0.0119249
$457$	0.243953	0.0114116	0.00570582	−	0.999984i	$-0.498184\pi$
$457$	0.243953	0.0114116	0.00570582	+	0.999984i	$0.498184\pi$
$458$	2.86258	0.133759
$459$	3.57201	0.166727
$460$	0.462531	0.0215656
$461$	0.447844	0.0208582	0.0104291	−	0.999946i	$-0.496680\pi$
$461$	0.447844	0.0208582	0.0104291	+	0.999946i	$0.496680\pi$
$462$	−1.87565	−0.0872633
$463$	33.4341	1.55382	0.776908	−	0.629615i	$-0.216787\pi$
$463$	33.4341	1.55382	0.776908	+	0.629615i	$0.216787\pi$
$464$	8.15894	0.378769
$465$	−1.99106	−0.0923330
$466$	−6.48488	−0.300406
$467$	26.7737	1.23894	0.619470	−	0.785020i	$-0.287347\pi$
$467$	26.7737	1.23894	0.619470	+	0.785020i	$0.287347\pi$
$468$	1.22486	0.0566193
$469$	−2.95172	−0.136298
$470$	0.814101	0.0375517
$471$	−11.7893	−0.543223
$472$	−5.56896	−0.256332
$473$	4.92470	0.226438
$474$	9.86962	0.453327
$475$	0.843098	0.0386840
$476$	0.634787	0.0290954
$477$	7.70783	0.352917
$478$	16.8360	0.770061
$479$	−21.7554	−0.994032	−0.497016	−	0.867741i	$-0.665571\pi$
$479$	−21.7554	−0.994032	−0.497016	+	0.867741i	$0.665571\pi$
$480$	0.310982	0.0141943
$481$	18.2043	0.830046
$482$	2.12359	0.0967271
$483$	3.33378	0.151692
$484$	−9.43046	−0.428657
$485$	2.70078	0.122636
$486$	−7.67531	−0.348159
$487$	−1.94342	−0.0880646	−0.0440323	−	0.999030i	$-0.514020\pi$
$487$	−1.94342	−0.0880646	−0.0440323	+	0.999030i	$0.514020\pi$
$488$	3.23438	0.146413
$489$	38.1105	1.72342
$490$	−0.207716	−0.00938364
$491$	−20.3172	−0.916904	−0.458452	−	0.888719i	$-0.651596\pi$
$491$	−20.3172	−0.916904	−0.458452	+	0.888719i	$0.651596\pi$
$492$	−15.0072	−0.676578
$493$	5.17919	0.233259
$494$	0.274652	0.0123572
$495$	0.197394	0.00887219
$496$	−6.40248	−0.287480
$497$	−9.79690	−0.439451
$498$	−2.85243	−0.127821
$499$	20.3656	0.911688	0.455844	−	0.890060i	$-0.349337\pi$
$499$	20.3656	0.911688	0.455844	+	0.890060i	$0.349337\pi$
$500$	2.06820	0.0924925
$501$	−6.29397	−0.281194
$502$	−4.50268	−0.200965
$503$	7.92151	0.353203	0.176601	−	0.984282i	$-0.443490\pi$
$503$	7.92151	0.353203	0.176601	+	0.984282i	$0.443490\pi$
$504$	−0.758538	−0.0337880
$505$	0.161181	0.00717247
$506$	−2.78970	−0.124017
$507$	15.5592	0.691008
$508$	4.52306	0.200678
$509$	31.2891	1.38687	0.693433	−	0.720521i	$-0.256097\pi$
$509$	31.2891	1.38687	0.693433	+	0.720521i	$0.256097\pi$
$510$	0.197407	0.00874134
$511$	16.4976	0.729812
$512$	1.00000	0.0441942
$513$	−0.957099	−0.0422569
$514$	−19.9032	−0.877894
$515$	−3.39041	−0.149399
$516$	−5.88517	−0.259080
$517$	−4.91016	−0.215948
$518$	−11.2737	−0.495336
$519$	16.8315	0.738820
$520$	0.335413	0.0147088
$521$	−21.2175	−0.929557	−0.464778	−	0.885427i	$-0.653866\pi$
$521$	−21.2175	−0.929557	−0.464778	+	0.885427i	$0.653866\pi$
$522$	−6.18887	−0.270879
$523$	6.41287	0.280415	0.140208	−	0.990122i	$-0.455223\pi$
$523$	6.41287	0.280415	0.140208	+	0.990122i	$0.455223\pi$
$524$	5.04659	0.220461
$525$	7.42116	0.323886
$526$	−4.59713	−0.200444
$527$	−4.06421	−0.177040
$528$	−1.87565	−0.0816273
$529$	−18.0416	−0.784417
$530$	2.11069	0.0916825
$531$	4.22427	0.183318
$532$	−0.170087	−0.00737422
$533$	−16.1862	−0.701102
$534$	12.8555	0.556312
$535$	−0.956722	−0.0413627
$536$	−2.95172	−0.127495
$537$	−11.3842	−0.491263
$538$	19.4403	0.838129
$539$	1.25281	0.0539625
$540$	−1.16884	−0.0502987
$541$	21.1419	0.908961	0.454481	−	0.890757i	$-0.349825\pi$
$541$	21.1419	0.908961	0.454481	+	0.890757i	$0.349825\pi$
$542$	−13.0032	−0.558535
$543$	−5.40508	−0.231954
$544$	0.634787	0.0272163
$545$	3.70250	0.158598
$546$	2.41755	0.103462
$547$	26.4324	1.13017	0.565084	−	0.825034i	$-0.308844\pi$
$547$	26.4324	1.13017	0.565084	+	0.825034i	$0.308844\pi$
$548$	−7.20198	−0.307653
$549$	−2.45340	−0.104708
$550$	−6.21002	−0.264796
$551$	−1.38773	−0.0591194
$552$	3.33378	0.141895
$553$	−6.59227	−0.280332
$554$	11.0275	0.468513
$555$	−3.50590	−0.148817
$556$	−17.9823	−0.762618
$557$	−28.8515	−1.22248	−0.611239	−	0.791446i	$-0.709329\pi$
$557$	−28.8515	−1.22248	−0.611239	+	0.791446i	$0.709329\pi$
$558$	4.85652	0.205593
$559$	−6.34751	−0.268471
$560$	−0.207716	−0.00877759
$561$	−1.19064	−0.0502688
$562$	−32.6215	−1.37606
$563$	7.87085	0.331717	0.165858	−	0.986150i	$-0.446961\pi$
$563$	7.87085	0.331717	0.165858	+	0.986150i	$0.446961\pi$
$564$	5.86779	0.247078
$565$	0.0922836	0.00388240
$566$	−9.92705	−0.417265
$567$	−6.14901	−0.258234
$568$	−9.79690	−0.411069
$569$	−19.0933	−0.800433	−0.400217	−	0.916421i	$-0.631065\pi$
$569$	−19.0933	−0.800433	−0.400217	+	0.916421i	$0.631065\pi$
$570$	−0.0528941	−0.00221549
$571$	−32.6941	−1.36820	−0.684102	−	0.729386i	$-0.739806\pi$
$571$	−32.6941	−1.36820	−0.684102	+	0.729386i	$0.739806\pi$
$572$	−2.02300	−0.0845861
$573$	13.2616	0.554012
$574$	10.0239	0.418388
$575$	11.0377	0.460303
$576$	−0.758538	−0.0316057
$577$	24.0999	1.00329	0.501645	−	0.865074i	$-0.332728\pi$
$577$	24.0999	1.00329	0.501645	+	0.865074i	$0.332728\pi$
$578$	−16.5970	−0.690346
$579$	5.89707	0.245074
$580$	−1.69474	−0.0703703
$581$	1.90524	0.0790426
$582$	19.4664	0.806909
$583$	−12.7304	−0.527239
$584$	16.4976	0.682677
$585$	−0.254423	−0.0105191
$586$	−23.8337	−0.984561
$587$	20.9312	0.863923	0.431962	−	0.901892i	$-0.357822\pi$
$587$	20.9312	0.863923	0.431962	+	0.901892i	$0.357822\pi$
$588$	−1.49715	−0.0617415
$589$	1.08898	0.0448707
$590$	1.15676	0.0476231
$591$	−34.3718	−1.41387
$592$	−11.2737	−0.463344
$593$	−1.65502	−0.0679635	−0.0339817	−	0.999422i	$-0.510819\pi$
$593$	−1.65502	−0.0679635	−0.0339817	+	0.999422i	$0.510819\pi$
$594$	7.04971	0.289253
$595$	−0.131855	−0.00540554
$596$	8.65050	0.354338
$597$	31.2200	1.27775
$598$	3.59568	0.147038
$599$	−9.60990	−0.392650	−0.196325	−	0.980539i	$-0.562901\pi$
$599$	−9.60990	−0.392650	−0.196325	+	0.980539i	$0.562901\pi$
$600$	7.42116	0.302968
$601$	27.1578	1.10779	0.553894	−	0.832587i	$-0.313141\pi$
$601$	27.1578	1.10779	0.553894	+	0.832587i	$0.313141\pi$
$602$	3.93091	0.160212
$603$	2.23899	0.0911788
$604$	4.81532	0.195933
$605$	1.95885	0.0796388
$606$	1.16174	0.0471926
$607$	16.7896	0.681469	0.340735	−	0.940159i	$-0.389324\pi$
$607$	16.7896	0.681469	0.340735	+	0.940159i	$0.389324\pi$
$608$	−0.170087	−0.00689795
$609$	−12.2152	−0.494984
$610$	−0.671831	−0.0272016
$611$	6.32876	0.256034
$612$	−0.481510	−0.0194639
$613$	−17.2757	−0.697761	−0.348880	−	0.937167i	$-0.613438\pi$
$613$	−17.2757	−0.697761	−0.348880	+	0.937167i	$0.613438\pi$
$614$	−6.54022	−0.263942
$615$	3.11724	0.125699
$616$	1.25281	0.0504773
$617$	3.81305	0.153508	0.0767538	−	0.997050i	$-0.475544\pi$
$617$	3.81305	0.153508	0.0767538	+	0.997050i	$0.475544\pi$
$618$	−24.4370	−0.983002
$619$	−13.2352	−0.531966	−0.265983	−	0.963978i	$-0.585696\pi$
$619$	−13.2352	−0.531966	−0.265983	+	0.963978i	$0.585696\pi$
$620$	1.32990	0.0534099
$621$	−12.5301	−0.502817
$622$	11.4769	0.460180
$623$	−8.58664	−0.344017
$624$	2.41755	0.0967795
$625$	24.3547	0.974187
$626$	3.51223	0.140377
$627$	0.319025	0.0127406
$628$	7.87450	0.314227
$629$	−7.15637	−0.285343
$630$	0.157560	0.00627735
$631$	21.0615	0.838445	0.419222	−	0.907884i	$-0.362303\pi$
$631$	21.0615	0.838445	0.419222	+	0.907884i	$0.362303\pi$
$632$	−6.59227	−0.262226
$633$	34.7945	1.38296
$634$	−21.7537	−0.863950
$635$	−0.939510	−0.0372833
$636$	15.2132	0.603243
$637$	−1.61477	−0.0639794
$638$	10.2216	0.404679
$639$	7.43132	0.293978
$640$	−0.207716	−0.00821069
$641$	−9.27475	−0.366330	−0.183165	−	0.983082i	$-0.558634\pi$
$641$	−9.27475	−0.366330	−0.183165	+	0.983082i	$0.558634\pi$
$642$	−6.89576	−0.272154
$643$	−26.3994	−1.04109	−0.520546	−	0.853834i	$-0.674271\pi$
$643$	−26.3994	−1.04109	−0.520546	+	0.853834i	$0.674271\pi$
$644$	−2.22675	−0.0877462
$645$	1.22244	0.0481336
$646$	−0.107969	−0.00424799
$647$	42.3291	1.66413	0.832064	−	0.554680i	$-0.187159\pi$
$647$	42.3291	1.66413	0.832064	+	0.554680i	$0.187159\pi$
$648$	−6.14901	−0.241556
$649$	−6.97687	−0.273866
$650$	8.00417	0.313949
$651$	9.58548	0.375685
$652$	−25.4553	−0.996908
$653$	8.01637	0.313705	0.156852	−	0.987622i	$-0.449865\pi$
$653$	8.01637	0.313705	0.156852	+	0.987622i	$0.449865\pi$
$654$	26.6865	1.04352
$655$	−1.04826	−0.0409587
$656$	10.0239	0.391366
$657$	−12.5141	−0.488220
$658$	−3.91930	−0.152790
$659$	27.6902	1.07866	0.539328	−	0.842096i	$-0.318678\pi$
$659$	27.6902	1.07866	0.539328	+	0.842096i	$0.318678\pi$
$660$	0.389603	0.0151653
$661$	6.45930	0.251238	0.125619	−	0.992079i	$-0.459908\pi$
$661$	6.45930	0.251238	0.125619	+	0.992079i	$0.459908\pi$
$662$	−9.53912	−0.370748
$663$	1.53463	0.0596001
$664$	1.90524	0.0739376
$665$	0.0353298	0.00137003
$666$	8.55149	0.331364
$667$	−18.1679	−0.703465
$668$	4.20396	0.162656
$669$	9.21338	0.356210
$670$	0.613119	0.0236869
$671$	4.05207	0.156429
$672$	−1.49715	−0.0577539
$673$	−29.8763	−1.15165	−0.575823	−	0.817575i	$-0.695318\pi$
$673$	−29.8763	−1.15165	−0.575823	+	0.817575i	$0.695318\pi$
$674$	19.1447	0.737427
$675$	−27.8927	−1.07359
$676$	−10.3925	−0.399712
$677$	−3.26896	−0.125636	−0.0628182	−	0.998025i	$-0.520009\pi$
$677$	−3.26896	−0.125636	−0.0628182	+	0.998025i	$0.520009\pi$
$678$	0.665152	0.0255450
$679$	−13.0023	−0.498983
$680$	−0.131855	−0.00505642
$681$	5.85629	0.224414
$682$	−8.02112	−0.307145
$683$	−12.1441	−0.464679	−0.232340	−	0.972635i	$-0.574638\pi$
$683$	−12.1441	−0.464679	−0.232340	+	0.972635i	$0.574638\pi$
$684$	0.129018	0.00493311
$685$	1.49596	0.0571578
$686$	1.00000	0.0381802
$687$	−4.28571	−0.163510
$688$	3.93091	0.149865
$689$	16.4084	0.625109
$690$	−0.692479	−0.0263622
$691$	9.88975	0.376224	0.188112	−	0.982148i	$-0.439763\pi$
$691$	9.88975	0.376224	0.188112	+	0.982148i	$0.439763\pi$
$692$	−11.2423	−0.427370
$693$	−0.950307	−0.0360992
$694$	2.40424	0.0912638
$695$	3.73520	0.141684
$696$	−12.2152	−0.463015
$697$	6.36301	0.241016
$698$	13.6670	0.517304
$699$	9.70885	0.367222
$700$	−4.95685	−0.187351
$701$	3.66496	0.138424	0.0692119	−	0.997602i	$-0.477952\pi$
$701$	3.66496	0.138424	0.0692119	+	0.997602i	$0.477952\pi$
$702$	−9.08646	−0.342946
$703$	1.91751	0.0723201
$704$	1.25281	0.0472172
$705$	−1.21883	−0.0459039
$706$	−22.6032	−0.850682
$707$	−0.775970	−0.0291834
$708$	8.33758	0.313345
$709$	−23.3705	−0.877697	−0.438848	−	0.898561i	$-0.644613\pi$
$709$	−23.3705	−0.877697	−0.438848	+	0.898561i	$0.644613\pi$
$710$	2.03497	0.0763711
$711$	5.00048	0.187533
$712$	−8.58664	−0.321798
$713$	14.2567	0.533918
$714$	−0.950372	−0.0355668
$715$	0.420210	0.0157150
$716$	7.60389	0.284171
$717$	−25.2060	−0.941337
$718$	31.8809	1.18978
$719$	20.0076	0.746159	0.373079	−	0.927799i	$-0.378302\pi$
$719$	20.0076	0.746159	0.373079	+	0.927799i	$0.378302\pi$
$720$	0.157560	0.00587192
$721$	16.3224	0.607877
$722$	−18.9711	−0.706030
$723$	−3.17934	−0.118241
$724$	3.61024	0.134174
$725$	−40.4427	−1.50200
$726$	14.1188	0.523999
$727$	−5.40026	−0.200285	−0.100142	−	0.994973i	$-0.531930\pi$
$727$	−5.40026	−0.200285	−0.100142	+	0.994973i	$0.531930\pi$
$728$	−1.61477	−0.0598473
$729$	29.9381	1.10882
$730$	−3.42682	−0.126832
$731$	2.49529	0.0922917
$732$	−4.84235	−0.178978
$733$	16.3342	0.603317	0.301659	−	0.953416i	$-0.402460\pi$
$733$	16.3342	0.603317	0.301659	+	0.953416i	$0.402460\pi$
$734$	25.6929	0.948341
$735$	0.310982	0.0114707
$736$	−2.22675	−0.0820791
$737$	−3.69796	−0.136216
$738$	−7.60347	−0.279888
$739$	8.31510	0.305876	0.152938	−	0.988236i	$-0.451127\pi$
$739$	8.31510	0.305876	0.152938	+	0.988236i	$0.451127\pi$
$740$	2.34172	0.0860832
$741$	−0.411195	−0.0151056
$742$	−10.1614	−0.373038
$743$	−48.6650	−1.78535	−0.892674	−	0.450704i	$-0.851173\pi$
$743$	−48.6650	−1.78535	−0.892674	+	0.450704i	$0.851173\pi$
$744$	9.58548	0.351421
$745$	−1.79685	−0.0658313
$746$	−7.50515	−0.274783
$747$	−1.44520	−0.0528770
$748$	0.795270	0.0290780
$749$	4.60592	0.168297
$750$	−3.09640	−0.113065
$751$	40.0102	1.45999	0.729997	−	0.683450i	$-0.239521\pi$
$751$	40.0102	1.45999	0.729997	+	0.683450i	$0.239521\pi$
$752$	−3.91930	−0.142922
$753$	6.74120	0.245663
$754$	−13.1748	−0.479798
$755$	−1.00022	−0.0364016
$756$	5.62710	0.204656
$757$	17.3945	0.632214	0.316107	−	0.948724i	$-0.397624\pi$
$757$	17.3945	0.632214	0.316107	+	0.948724i	$0.397624\pi$
$758$	23.2831	0.845679
$759$	4.17661	0.151601
$760$	0.0353298	0.00128155
$761$	−4.81856	−0.174673	−0.0873364	−	0.996179i	$-0.527835\pi$
$761$	−4.81856	−0.174673	−0.0873364	+	0.996179i	$0.527835\pi$
$762$	−6.77170	−0.245313
$763$	−17.8248	−0.645303
$764$	−8.85791	−0.320468
$765$	0.100017	0.00361613
$766$	−6.85794	−0.247787
$767$	8.99258	0.324703
$768$	−1.49715	−0.0540238
$769$	−6.86097	−0.247413	−0.123707	−	0.992319i	$-0.539478\pi$
$769$	−6.86097	−0.247413	−0.123707	+	0.992319i	$0.539478\pi$
$770$	−0.260229	−0.00937801
$771$	29.7982	1.07315
$772$	−3.93886	−0.141763
$773$	−22.3728	−0.804693	−0.402347	−	0.915487i	$-0.631805\pi$
$773$	−22.3728	−0.804693	−0.402347	+	0.915487i	$0.631805\pi$
$774$	−2.98175	−0.107177
$775$	31.7362	1.14000
$776$	−13.0023	−0.466756
$777$	16.8784	0.605508
$778$	−18.6914	−0.670120
$779$	−1.70493	−0.0610855
$780$	−0.502164	−0.0179803
$781$	−12.2737	−0.439187
$782$	−1.41351	−0.0505471
$783$	45.9112	1.64073
$784$	1.00000	0.0357143
$785$	−1.63566	−0.0583791
$786$	−7.55551	−0.269496
$787$	33.4426	1.19210	0.596051	−	0.802947i	$-0.296736\pi$
$787$	33.4426	1.19210	0.596051	+	0.802947i	$0.296736\pi$
$788$	22.9581	0.817849
$789$	6.88260	0.245027
$790$	1.36932	0.0487181
$791$	−0.444278	−0.0157967
$792$	−0.950307	−0.0337677
$793$	−5.22277	−0.185466
$794$	−7.92237	−0.281154
$795$	−3.16002	−0.112074
$796$	−20.8529	−0.739112
$797$	41.4161	1.46703	0.733517	−	0.679671i	$-0.237877\pi$
$797$	41.4161	1.46703	0.733517	+	0.679671i	$0.237877\pi$
$798$	0.254647	0.00901439
$799$	−2.48792	−0.0880163
$800$	−4.95685	−0.175251
$801$	6.51329	0.230136
$802$	−26.5403	−0.937172
$803$	20.6685	0.729374
$804$	4.41917	0.155852
$805$	0.462531	0.0163021
$806$	10.3385	0.364159
$807$	−29.1050	−1.02454
$808$	−0.775970	−0.0272985
$809$	46.8159	1.64596	0.822979	−	0.568072i	$-0.192310\pi$
$809$	46.8159	1.64596	0.822979	+	0.568072i	$0.192310\pi$
$810$	1.27725	0.0448778
$811$	24.9974	0.877779	0.438889	−	0.898541i	$-0.355372\pi$
$811$	24.9974	0.877779	0.438889	+	0.898541i	$0.355372\pi$
$812$	8.15894	0.286323
$813$	19.4677	0.682763
$814$	−14.1238	−0.495039
$815$	5.28747	0.185212
$816$	−0.950372	−0.0332697
$817$	−0.668598	−0.0233913
$818$	29.1109	1.01784
$819$	1.22486	0.0428002
$820$	−2.08211	−0.0727105
$821$	23.1777	0.808907	0.404454	−	0.914559i	$-0.367462\pi$
$821$	23.1777	0.808907	0.404454	+	0.914559i	$0.367462\pi$
$822$	10.7824	0.376081
$823$	−18.2880	−0.637478	−0.318739	−	0.947843i	$-0.603259\pi$
$823$	−18.2880	−0.637478	−0.318739	+	0.947843i	$0.603259\pi$
$824$	16.3224	0.568616
$825$	9.29734	0.323692
$826$	−5.56896	−0.193769
$827$	29.7126	1.03321	0.516604	−	0.856225i	$-0.327196\pi$
$827$	29.7126	1.03321	0.516604	+	0.856225i	$0.327196\pi$
$828$	1.68907	0.0586994
$829$	8.66340	0.300892	0.150446	−	0.988618i	$-0.451929\pi$
$829$	8.66340	0.300892	0.150446	+	0.988618i	$0.451929\pi$
$830$	−0.395748	−0.0137366
$831$	−16.5098	−0.572719
$832$	−1.61477	−0.0559820
$833$	0.634787	0.0219941
$834$	26.9222	0.932238
$835$	−0.873230	−0.0302194
$836$	−0.213088	−0.00736980
$837$	−36.0274	−1.24529
$838$	−35.5714	−1.22879
$839$	28.5938	0.987168	0.493584	−	0.869698i	$-0.335686\pi$
$839$	28.5938	0.987168	0.493584	+	0.869698i	$0.335686\pi$
$840$	0.310982	0.0107299
$841$	37.5684	1.29546
$842$	−30.6682	−1.05690
$843$	48.8393	1.68212
$844$	−23.2405	−0.799970
$845$	2.15869	0.0742612
$846$	2.97294	0.102212
$847$	−9.43046	−0.324034
$848$	−10.1614	−0.348945
$849$	14.8623	0.510073
$850$	−3.14655	−0.107926
$851$	25.1036	0.860541
$852$	14.6674	0.502498
$853$	−52.6985	−1.80436	−0.902181	−	0.431359i	$-0.858034\pi$
$853$	−52.6985	−1.80436	−0.902181	+	0.431359i	$0.858034\pi$
$854$	3.23438	0.110678
$855$	−0.0267990	−0.000916507 0
$856$	4.60592	0.157427
$857$	−11.8089	−0.403386	−0.201693	−	0.979449i	$-0.564644\pi$
$857$	−11.8089	−0.403386	−0.201693	+	0.979449i	$0.564644\pi$
$858$	3.02874	0.103400
$859$	22.5446	0.769213	0.384607	−	0.923081i	$-0.374337\pi$
$859$	22.5446	0.769213	0.384607	+	0.923081i	$0.374337\pi$
$860$	−0.816512	−0.0278428
$861$	−15.0072	−0.511445
$862$	−1.00000	−0.0340601
$863$	6.02572	0.205118	0.102559	−	0.994727i	$-0.467297\pi$
$863$	6.02572	0.205118	0.102559	+	0.994727i	$0.467297\pi$
$864$	5.62710	0.191438
$865$	2.33521	0.0793996
$866$	23.8209	0.809466
$867$	24.8483	0.843892
$868$	−6.40248	−0.217314
$869$	−8.25889	−0.280164
$870$	2.53728	0.0860220
$871$	4.76635	0.161501
$872$	−17.8248	−0.603625
$873$	9.86274	0.333803
$874$	0.378742	0.0128111
$875$	2.06820	0.0699178
$876$	−24.6994	−0.834517
$877$	−45.2156	−1.52682	−0.763412	−	0.645912i	$-0.776477\pi$
$877$	−45.2156	−1.52682	−0.763412	+	0.645912i	$0.776477\pi$
$878$	−30.5769	−1.03192
$879$	35.6827	1.20355
$880$	−0.260229	−0.00877233
$881$	24.1915	0.815031	0.407515	−	0.913198i	$-0.366395\pi$
$881$	24.1915	0.815031	0.407515	+	0.913198i	$0.366395\pi$
$882$	−0.758538	−0.0255413
$883$	49.3911	1.66214	0.831072	−	0.556165i	$-0.187728\pi$
$883$	49.3911	1.66214	0.831072	+	0.556165i	$0.187728\pi$
$884$	−1.02503	−0.0344756
$885$	−1.73185	−0.0582154
$886$	22.9515	0.771071
$887$	12.9057	0.433330	0.216665	−	0.976246i	$-0.430482\pi$
$887$	12.9057	0.433330	0.216665	+	0.976246i	$0.430482\pi$
$888$	16.8784	0.566401
$889$	4.52306	0.151698
$890$	1.78358	0.0597858
$891$	−7.70356	−0.258079
$892$	−6.15394	−0.206049
$893$	0.666624	0.0223077
$894$	−12.9511	−0.433150
$895$	−1.57945	−0.0527951
$896$	1.00000	0.0334077
$897$	−5.38328	−0.179743
$898$	−13.7725	−0.459594
$899$	−52.2375	−1.74222
$900$	3.75996	0.125332
$901$	−6.45034	−0.214892
$902$	12.5580	0.418137
$903$	−5.88517	−0.195846
$904$	−0.444278	−0.0147765
$905$	−0.749904	−0.0249276
$906$	−7.20926	−0.239512
$907$	47.2781	1.56984	0.784922	−	0.619595i	$-0.212703\pi$
$907$	47.2781	1.56984	0.784922	+	0.619595i	$0.212703\pi$
$908$	−3.91162	−0.129812
$909$	0.588603	0.0195227
$910$	0.335413	0.0111188
$911$	49.0114	1.62382	0.811911	−	0.583782i	$-0.198428\pi$
$911$	49.0114	1.62382	0.811911	+	0.583782i	$0.198428\pi$
$912$	0.254647	0.00843219
$913$	2.38691	0.0789952
$914$	0.243953	0.00806924
$915$	1.00583	0.0332518
$916$	2.86258	0.0945822
$917$	5.04659	0.166653
$918$	3.57201	0.117894
$919$	33.0055	1.08875	0.544376	−	0.838841i	$-0.316767\pi$
$919$	33.0055	1.08875	0.544376	+	0.838841i	$0.316767\pi$
$920$	0.462531	0.0152492
$921$	9.79169	0.322647
$922$	0.447844	0.0147490
$923$	15.8197	0.520713
$924$	−1.87565	−0.0617044
$925$	55.8819	1.83738
$926$	33.4341	1.09871
$927$	−12.3811	−0.406650
$928$	8.15894	0.267830
$929$	48.6374	1.59574	0.797870	−	0.602829i	$-0.205960\pi$
$929$	48.6374	1.59574	0.797870	+	0.602829i	$0.205960\pi$
$930$	−1.99106	−0.0652893
$931$	−0.170087	−0.00557439
$932$	−6.48488	−0.212419
$933$	−17.1826	−0.562533
$934$	26.7737	0.876063
$935$	−0.165190	−0.00540229
$936$	1.22486	0.0400359
$937$	−10.6806	−0.348921	−0.174461	−	0.984664i	$-0.555818\pi$
$937$	−10.6806	−0.348921	−0.174461	+	0.984664i	$0.555818\pi$
$938$	−2.95172	−0.0963771
$939$	−5.25834	−0.171599
$940$	0.814101	0.0265530
$941$	−43.8971	−1.43101	−0.715503	−	0.698610i	$-0.753802\pi$
$941$	−43.8971	−1.43101	−0.715503	+	0.698610i	$0.753802\pi$
$942$	−11.7893	−0.384117
$943$	−22.3206	−0.726859
$944$	−5.56896	−0.181254
$945$	−1.16884	−0.0380223
$946$	4.92470	0.160116
$947$	−19.6246	−0.637714	−0.318857	−	0.947803i	$-0.603299\pi$
$947$	−19.6246	−0.637714	−0.318857	+	0.947803i	$0.603299\pi$
$948$	9.86962	0.320550
$949$	−26.6398	−0.864766
$950$	0.843098	0.0273537
$951$	32.5686	1.05611
$952$	0.634787	0.0205736
$953$	−1.53663	−0.0497763	−0.0248882	−	0.999690i	$-0.507923\pi$
$953$	−1.53663	−0.0497763	−0.0248882	+	0.999690i	$0.507923\pi$
$954$	7.70783	0.249550
$955$	1.83993	0.0595386
$956$	16.8360	0.544515
$957$	−15.3033	−0.494687
$958$	−21.7554	−0.702886
$959$	−7.20198	−0.232564
$960$	0.310982	0.0100369
$961$	9.99177	0.322315
$962$	18.2043	0.586931
$963$	−3.49376	−0.112585
$964$	2.12359	0.0683964
$965$	0.818163	0.0263376
$966$	3.33378	0.107263
$967$	−2.66355	−0.0856539	−0.0428269	−	0.999083i	$-0.513636\pi$
$967$	−2.66355	−0.0856539	−0.0428269	+	0.999083i	$0.513636\pi$
$968$	−9.43046	−0.303106
$969$	0.161646	0.00519283
$970$	2.70078	0.0867170
$971$	14.0505	0.450903	0.225452	−	0.974254i	$-0.427614\pi$
$971$	14.0505	0.450903	0.225452	+	0.974254i	$0.427614\pi$
$972$	−7.67531	−0.246186
$973$	−17.9823	−0.576485
$974$	−1.94342	−0.0622711
$975$	−11.9835	−0.383778
$976$	3.23438	0.103530
$977$	−35.0991	−1.12292	−0.561460	−	0.827504i	$-0.689760\pi$
$977$	−35.0991	−1.12292	−0.561460	+	0.827504i	$0.689760\pi$
$978$	38.1105	1.21864
$979$	−10.7575	−0.343810
$980$	−0.207716	−0.00663524
$981$	13.5208	0.431687
$982$	−20.3172	−0.648349
$983$	0.974901	0.0310945	0.0155473	−	0.999879i	$-0.495051\pi$
$983$	0.974901	0.0310945	0.0155473	+	0.999879i	$0.495051\pi$
$984$	−15.0072	−0.478413
$985$	−4.76876	−0.151945
$986$	5.17919	0.164939
$987$	5.86779	0.186774
$988$	0.274652	0.00873783
$989$	−8.75316	−0.278334
$990$	0.197394	0.00627358
$991$	30.6706	0.974283	0.487142	−	0.873323i	$-0.338040\pi$
$991$	30.6706	0.974283	0.487142	+	0.873323i	$0.338040\pi$
$992$	−6.40248	−0.203279
$993$	14.2815	0.453210
$994$	−9.79690	−0.310739
$995$	4.33148	0.137317
$996$	−2.85243	−0.0903827
$997$	−10.2699	−0.325249	−0.162625	−	0.986688i	$-0.551996\pi$
$997$	−10.2699	−0.325249	−0.162625	+	0.986688i	$0.551996\pi$
$998$	20.3656	0.644661
$999$	−63.4380	−2.00709

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6034.2.a.m.1.7	✓	21

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6034.2.a.m.1.7	✓	21	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 6034 = 2 \cdot 7 \cdot 431 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6034.a (trivial)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} -1.49715 q^{3} +1.00000 q^{4} -0.207716 q^{5} -1.49715 q^{6} +1.00000 q^{7} +1.00000 q^{8} -0.758538 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} -1.49715 q^{3} +1.00000 q^{4} -0.207716 q^{5} -1.49715 q^{6} +1.00000 q^{7} +1.00000 q^{8} -0.758538 q^{9} -0.207716 q^{10} +1.25281 q^{11} -1.49715 q^{12} -1.61477 q^{13} +1.00000 q^{14} +0.310982 q^{15} +1.00000 q^{16} +0.634787 q^{17} -0.758538 q^{18} -0.170087 q^{19} -0.207716 q^{20} -1.49715 q^{21} +1.25281 q^{22} -2.22675 q^{23} -1.49715 q^{24} -4.95685 q^{25} -1.61477 q^{26} +5.62710 q^{27} +1.00000 q^{28} +8.15894 q^{29} +0.310982 q^{30} -6.40248 q^{31} +1.00000 q^{32} -1.87565 q^{33} +0.634787 q^{34} -0.207716 q^{35} -0.758538 q^{36} -11.2737 q^{37} -0.170087 q^{38} +2.41755 q^{39} -0.207716 q^{40} +10.0239 q^{41} -1.49715 q^{42} +3.93091 q^{43} +1.25281 q^{44} +0.157560 q^{45} -2.22675 q^{46} -3.91930 q^{47} -1.49715 q^{48} +1.00000 q^{49} -4.95685 q^{50} -0.950372 q^{51} -1.61477 q^{52} -10.1614 q^{53} +5.62710 q^{54} -0.260229 q^{55} +1.00000 q^{56} +0.254647 q^{57} +8.15894 q^{58} -5.56896 q^{59} +0.310982 q^{60} +3.23438 q^{61} -6.40248 q^{62} -0.758538 q^{63} +1.00000 q^{64} +0.335413 q^{65} -1.87565 q^{66} -2.95172 q^{67} +0.634787 q^{68} +3.33378 q^{69} -0.207716 q^{70} -9.79690 q^{71} -0.758538 q^{72} +16.4976 q^{73} -11.2737 q^{74} +7.42116 q^{75} -0.170087 q^{76} +1.25281 q^{77} +2.41755 q^{78} -6.59227 q^{79} -0.207716 q^{80} -6.14901 q^{81} +10.0239 q^{82} +1.90524 q^{83} -1.49715 q^{84} -0.131855 q^{85} +3.93091 q^{86} -12.2152 q^{87} +1.25281 q^{88} -8.58664 q^{89} +0.157560 q^{90} -1.61477 q^{91} -2.22675 q^{92} +9.58548 q^{93} -3.91930 q^{94} +0.0353298 q^{95} -1.49715 q^{96} -13.0023 q^{97} +1.00000 q^{98} -0.950307 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 21 q + 21 q^{2} - 6 q^{3} + 21 q^{4} - 11 q^{5} - 6 q^{6} + 21 q^{7} + 21 q^{8} + 5 q^{9}+O(q^{10}) \) 21 * q + 21 * q^2 - 6 * q^3 + 21 * q^4 - 11 * q^5 - 6 * q^6 + 21 * q^7 + 21 * q^8 + 5 * q^9	\( 21 q + 21 q^{2} - 6 q^{3} + 21 q^{4} - 11 q^{5} - 6 q^{6} + 21 q^{7} + 21 q^{8} + 5 q^{9} - 11 q^{10} - 34 q^{11} - 6 q^{12} - 19 q^{13} + 21 q^{14} - 24 q^{15} + 21 q^{16} - 17 q^{17} + 5 q^{18} - 15 q^{19} - 11 q^{20} - 6 q^{21} - 34 q^{22} - 32 q^{23} - 6 q^{24} + 6 q^{25} - 19 q^{26} - 3 q^{27} + 21 q^{28} - 46 q^{29} - 24 q^{30} + 7 q^{31} + 21 q^{32} - 13 q^{33} - 17 q^{34} - 11 q^{35} + 5 q^{36} - 34 q^{37} - 15 q^{38} - 25 q^{39} - 11 q^{40} - 27 q^{41} - 6 q^{42} - 47 q^{43} - 34 q^{44} - 13 q^{45} - 32 q^{46} - 7 q^{47} - 6 q^{48} + 21 q^{49} + 6 q^{50} - 29 q^{51} - 19 q^{52} - 57 q^{53} - 3 q^{54} + 17 q^{55} + 21 q^{56} - 28 q^{57} - 46 q^{58} - 30 q^{59} - 24 q^{60} - 17 q^{61} + 7 q^{62} + 5 q^{63} + 21 q^{64} - 40 q^{65} - 13 q^{66} - 38 q^{67} - 17 q^{68} - 13 q^{69} - 11 q^{70} - 66 q^{71} + 5 q^{72} - 15 q^{73} - 34 q^{74} + 15 q^{75} - 15 q^{76} - 34 q^{77} - 25 q^{78} - 17 q^{79} - 11 q^{80} - 11 q^{81} - 27 q^{82} - 19 q^{83} - 6 q^{84} - 28 q^{85} - 47 q^{86} + 45 q^{87} - 34 q^{88} - 39 q^{89} - 13 q^{90} - 19 q^{91} - 32 q^{92} - 25 q^{93} - 7 q^{94} - 35 q^{95} - 6 q^{96} + 21 q^{98} - 52 q^{99}+O(q^{100}) \) 21 * q + 21 * q^2 - 6 * q^3 + 21 * q^4 - 11 * q^5 - 6 * q^6 + 21 * q^7 + 21 * q^8 + 5 * q^9 - 11 * q^10 - 34 * q^11 - 6 * q^12 - 19 * q^13 + 21 * q^14 - 24 * q^15 + 21 * q^16 - 17 * q^17 + 5 * q^18 - 15 * q^19 - 11 * q^20 - 6 * q^21 - 34 * q^22 - 32 * q^23 - 6 * q^24 + 6 * q^25 - 19 * q^26 - 3 * q^27 + 21 * q^28 - 46 * q^29 - 24 * q^30 + 7 * q^31 + 21 * q^32 - 13 * q^33 - 17 * q^34 - 11 * q^35 + 5 * q^36 - 34 * q^37 - 15 * q^38 - 25 * q^39 - 11 * q^40 - 27 * q^41 - 6 * q^42 - 47 * q^43 - 34 * q^44 - 13 * q^45 - 32 * q^46 - 7 * q^47 - 6 * q^48 + 21 * q^49 + 6 * q^50 - 29 * q^51 - 19 * q^52 - 57 * q^53 - 3 * q^54 + 17 * q^55 + 21 * q^56 - 28 * q^57 - 46 * q^58 - 30 * q^59 - 24 * q^60 - 17 * q^61 + 7 * q^62 + 5 * q^63 + 21 * q^64 - 40 * q^65 - 13 * q^66 - 38 * q^67 - 17 * q^68 - 13 * q^69 - 11 * q^70 - 66 * q^71 + 5 * q^72 - 15 * q^73 - 34 * q^74 + 15 * q^75 - 15 * q^76 - 34 * q^77 - 25 * q^78 - 17 * q^79 - 11 * q^80 - 11 * q^81 - 27 * q^82 - 19 * q^83 - 6 * q^84 - 28 * q^85 - 47 * q^86 + 45 * q^87 - 34 * q^88 - 39 * q^89 - 13 * q^90 - 19 * q^91 - 32 * q^92 - 25 * q^93 - 7 * q^94 - 35 * q^95 - 6 * q^96 + 21 * q^98 - 52 * q^99

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